Medical Training through Navy vs. Air Force vs. Army? What are the differences? What are the steps?

Hello, I've had my heart set on becoming a doctor since I was a little kid but have always wanted to have that experience of being part of something bigger than myself.

I've always wanted to help people, interned at many hospitals, and even some of the worst wounds don't make me cringe. My grades are average (about a 3.4 but I'm going to try a lot harder this semester), and I'm about to enter my sophomore year in college. I plan on finishing my undergrad before I make any decisions and I'm majoring in Bio-medical Science which is pretty much the same as pre-med but my school offers all sorts so I took this route.

I'd love to be stationed anywhere in the world really, whether in the U.S. or across the Atlantic. I would not like to face combat situations because I don't believe in taking lives, but saving them. I'd like to work with people in third world countries that can't afford medical care (I'm not positive but I hear the Navy and people with the Red Cross are able to do this). I am not very certain I'd be able to live on a ship for a few months at a time though.

I just want to know what are the differences between the 3, when I sign up do I go through med training first or after my service, what kind of training, physical and academic, would I be going through? Which do you think would best work with my type of personality? Do you have any person experience or know anyone who has/ what did you or they think about it?